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An algorithm for robust initial orbit determination (IOD) under perturbed orbital dynamics is presented. By leveraging map inversion techniques defined in the algebra of Taylor polynomials, this tool returns a highly accurate solution to the IOD problem and estimates a range centered on the aforementioned solution in which the true orbit should lie. To meet the specified accuracy requirements, automatic domain splitting is used to wrap the IOD routines and ensure that the local truncation error, introduced by a polynomial representation of the state estimate, remains below a predefined threshold. The algorithm is presented for three types of ground-based sensors, namely range radars, Doppler-only radars, and optical telescopes, by considering their different constraints in terms of available measurements and sensor noise. Finally, the improvement in performance with respect to a Keplerian-based IOD solution is demonstrated using large-scale numerical simulations over a subset of tracked objects in low Earth orbit.
ESA Space Debris Office. ESA's annual space environment report. Technical Report. Paris: European Space Agency, 2022.
Laplace, P. S. Traité de Mécanique Céleste (Tome Premier). Paris: Imprimerie de Crapelet Chez J. B. M. Duprat, 1798. (in French)
Gauss, C. F. Theoria Motus Corporum Coelestium in Sectionibus Conicis Solem Ambientium. Hamburg, Germany: Perthes et Besser, 1809.
Escobal, P. R. Methods of Orbit Determination. New York: John Wiley & Sons, 1965.
Baker, R. M. L. Jr., Jacoby, N. H. Jr. Preliminary orbit-determination method having no co-planar singularity. Celestial Mechanics, 1977, 15(2): 137–160.
Gooding, R. H. A new procedure for the solution of the classical problem of minimal orbit determination from three lines of sight. Celestial Mechanics and Dynamical Astronomy, 1996, 66(4): 387–423.
Karimi, R. R., Mortari, D. Initial orbit determination using multiple observations. Celestial Mechanics and Dynamical Astronomy, 2011, 109(2): 167–180.
Izzo, D. Revisiting Lambert's problem. Celestial Mechanics and Dynamical Astronomy, 2015, 121(1): 1–15.
Gibbs, J. W. On the determination of elliptic orbits from three complete observations. Memoirs of the National Academy of Sciences, 1889, 4(2): 79–104.
Herrick, S. Astrodynamics (Vol. 1, Orbit Determination, Space Navigation, Celestial Mechanics). London: Van Nostrand Reinhold Company, 1971.
Christian, J. A., Parker, W. E. Initial orbit determination from bearing and range-rate measurements using the orbital hodograph. Journal of Guidance, Control, and Dynamics, 2021, 44(2): 370–378.
Wittig, A., Di Lizia, P., Armellin, R., Makino, K., Bernelli-Zazzera, F., Berz, M. Propagation of large uncertainty sets in orbital dynamics by automatic domain splitting. Celestial Mechanics and Dynamical Astronomy, 2015, 122(3): 239–261.
Pirovano, L., Santeramo, D. A., Armellin, R., Lizia, P., Wittig, A. Probabilistic data association: The orbit set. Celestial Mechanics and Dynamical Astronomy, 2020, 132(2): 15.
Armellin, R., Di Lizia, P. Probabilistic optical and radar initial orbit determination. Journal of Guidance, Control, and Dynamics, 2018, 41(1): 101–118.
Losacco, M., Armellin, R., Yanez, C., Pirovano, L., Lizy-Destrez, S., Sanfedino, F. Robust initial orbit determination for surveillance Doppler-only radars. IEEE Transactions on Aerospace and Electronic Systems, 2023, doi: 10.1109/TAES.2023.3249667.
Berz, M. Modern Map Methods in Particle Beam Physics. London: Academic Press, 1999.
Valli, M., Armellin, R., Di Lizia, P., Lavagna, M. R. Nonlinear mapping of uncertainties in celestial mechanics. Journal of Guidance, Control, and Dynamics, 2013, 36(1): 48–63.
Armellin, R., Gondelach, D. J., Juan, J. F. S. Multiple revolution perturbed Lambert problem solvers. Journal of Guidance, Control, and Dynamics, 2018, 41(9): 1–31.
Vallado, D. A. Fundamentals of Astrodynamics and Applications, 4th edn. Hawthorne, USA: Microcosm Press, 2013.
